On Wed, Dec 18, 2013 at 8:01 PM, meekerdb <meeke...@verizon.net> wrote:
> On 12/18/2013 4:27 PM, Stephen Paul King wrote:
> Ever attempt to do a particular calculation with an actual infinite
> dimensional Hilbert space?
> Why not? Sure, you can mod out (using symmetries and other tricks) all
> of the infinite dimensions except some finite subset,
> You can calculate all the eigenfunctions of a finite square well.
> but that is the act that introduces the bias that I am pointing at! The
> actual Hilbert spaces used to do calculi are finite dimensional.
> Even if you only find a finite subset of eigenfunctions, the calculation
> is still done in an infinite dimensional space. If you create a wave
> packet it consists of infinitely many momentum eigenfunctions. I don't see
> that cutting the
What else did you meant to write?
> No, Choosing a basis and choosing a coordinate system is NOT a
> convenience. You must do it.
> Try reading Robert Wald's "Quantum Field Theory in Curved Spacetime". He
> seldom chooses a coordinate system.
> I have.
> Especially in GR, where one cannot define the manifold unless there is a
> choice of coordinate system on the patches of local space-time used to
> define the manifold - which is then run through the diffeomorphism mill...
> AFAIK, there is no global manifold that can be defined that does not
> involve the requirement of stitching together of local patches of
> space-time (defined per individual events) into manifolds of arbitrary
> But that doesn't require choosing a specific coordinate system, and in
> fact for most manifolds it is impossible to choose a single coordinate
> What must be remembered is that the "stitching operation" is very
> restrictive, one cannot connect patches that have events with
> different (other than an infinitesimal) values of momenta and position
> associated with each. The math of GR is amazing once one is familiar with
> ?? Coordinate patches have momenta?? That's amazing all right.
that is not what I wrote.
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Stephen Paul King
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